A classical mechanics problem by Ajay Venugopal

I applied formula integral(F.ds) / integral(ds) , and wrote F = m . v .dv/ds , which cancels ds in numerator , and integrate it woth proper limits of 300m/s as lower limit and 0 as higher limit, also convert the g to kg, cm to metre.

$W = E_{2} - E_{1}$ $F \times s = \frac {1}{2} \times m \times ( v_{2}^{2} - v_{1}^{2} )$ $F \times 3 \times 10^{-2} = \frac {1}{2} \times 20 \times 10^{-3} \times ( 300^{2} - 0^{2} )$ $F = \frac {9 \times 10^{4}}{3}$ $F = 3 \times 10^{4}$